Newform search results

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank
Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 111 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.1.g.a	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)		$1$		\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
152.1.g.b	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
152.1.k.a	$152$	$1$	152.k	152.k	$6$	$2$	$1$	$0.076$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)		$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
152.1.u.a	$152$	$1$	152.u	152.u	$18$	$6$	$1$	$0.076$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$1$		\(q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots\)
152.2.a.a	$152$	$2$	152.a	1.a	$1$	$1$	$1$	$1.214$	\(\Q\)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
152.2.a.b	$152$	$2$	152.a	1.a	$1$	$1$	$1$	$1.214$	\(\Q\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
152.2.a.c	$152$	$2$	152.a	1.a	$1$	$3$	$3$	$1.214$	3.3.961.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
152.2.b.a	$152$	$2$	152.b	152.b	$2$	$2$	$2$	$1.214$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+2\beta q^{3}-2q^{4}-4q^{6}-2\beta q^{8}+\cdots\)
152.2.b.b	$152$	$2$	152.b	152.b	$2$	$4$	$4$	$1.214$	\(\Q(\sqrt{-3}, \sqrt{5})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots\)
152.2.b.c	$152$	$2$	152.b	152.b	$2$	$12$	$12$	$1.214$	12.0.\(\cdots\).1	$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)
152.2.c.a	$152$	$2$	152.c	8.b	$2$	$2$	$2$	$1.214$	\(\Q(\sqrt{-1}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\cdots\)
152.2.c.b	$152$	$2$	152.c	8.b	$2$	$16$	$16$	$1.214$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
152.2.i.a	$152$	$2$	152.i	19.c	$3$	$2$	$1$	$1.214$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.b	$152$	$2$	152.i	19.c	$3$	$2$	$1$	$1.214$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.c	$152$	$2$	152.i	19.c	$3$	$6$	$3$	$1.214$	6.0.2696112.1	$_{}$	None	None		$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.2.o.a	$152$	$2$	152.o	152.o	$6$	$4$	$2$	$1.214$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$_{}$	None	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.b	$152$	$2$	152.o	152.o	$6$	$4$	$2$	$1.214$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.c	$152$	$2$	152.o	152.o	$6$	$28$	$14$	$1.214$		$_{}$	None	None		$4$	$0$	\(-3\)	\(-6\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
152.2.p.a	$152$	$2$	152.p	152.p	$6$	$36$	$18$	$1.214$		$_{}$	None	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{6}]$
152.2.q.a	$152$	$2$	152.q	19.e	$9$	$6$	$1$	$1.214$	\(\Q(\zeta_{18})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-6\)	\(6\)	\(3\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots\)
152.2.q.b	$152$	$2$	152.q	19.e	$9$	$6$	$1$	$1.214$	\(\Q(\zeta_{18})\)	$_{}$	None	None		$2$	$0$	\(0\)	\(9\)	\(-6\)	\(6\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots\)
152.2.q.c	$152$	$2$	152.q	19.e	$9$	$18$	$3$	$1.214$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)		$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
152.2.t.a	$152$	$2$	152.t	152.t	$18$	$108$	$18$	$1.214$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
152.2.v.a	$152$	$2$	152.v	152.v	$18$	$12$	$2$	$1.214$	12.0.\(\cdots\).1	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{18}]$	\(q-\beta _{11}q^{2}+(\beta _{1}+\beta _{3}-\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots\)
152.2.v.b	$152$	$2$	152.v	152.v	$18$	$96$	$16$	$1.214$		$_{}$	None	None		$4$	$0$	\(-6\)	\(-6\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
152.3.e.a	$152$	$3$	152.e	19.b	$2$	$2$	$2$	$4.142$	\(\Q(\sqrt{-2}) \)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(22\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+7q^{5}+11q^{7}-23q^{9}+3q^{11}+\cdots\)
152.3.e.b	$152$	$3$	152.e	19.b	$2$	$8$	$8$	$4.142$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(-6\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots\)
152.3.f.a	$152$	$3$	152.f	8.d	$2$	$36$	$36$	$4.142$		$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
152.3.g.a	$152$	$3$	152.g	152.g	$2$	$3$	$3$	$4.142$	3.3.4104.1	$_{}$	\(\Q(\sqrt{-38}) \)	None	✓	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.b	$152$	$3$	152.g	152.g	$2$	$3$	$3$	$4.142$	3.3.4104.1	$_{}$	\(\Q(\sqrt{-38}) \)	None	✓	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)		$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.c	$152$	$3$	152.g	152.g	$2$	$32$	$32$	$4.142$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{2}]$
152.3.k.a	$152$	$3$	152.k	152.k	$6$	$4$	$2$	$4.142$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(4\)	\(-2\)	\(0\)	\(0\)		$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{6}]$	\(q+2\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+4\beta _{1}+\cdots)q^{4}+\cdots\)
152.3.k.b	$152$	$3$	152.k	152.k	$6$	$72$	$36$	$4.142$		$_{}$	None	None		$4$	$0$	\(-5\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
152.3.l.a	$152$	$3$	152.l	152.l	$6$	$76$	$38$	$4.142$		$_{}$	None	None		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(-8\)			$\mathrm{SU}(2)[C_{6}]$
152.3.n.a	$152$	$3$	152.n	19.d	$6$	$20$	$10$	$4.142$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-16\)		$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{3}+\beta _{19}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
152.3.r.a	$152$	$3$	152.r	19.f	$18$	$60$	$10$	$4.142$		$_{}$	None	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
152.3.s.a	$152$	$3$	152.s	152.s	$18$	$228$	$38$	$4.142$		$_{}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{18}]$
152.3.u.a	$152$	$3$	152.u	152.u	$18$	$12$	$2$	$4.142$	12.0.\(\cdots\).1	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$2^{6}\cdot 3$	$\mathrm{U}(1)[D_{18}]$	\(q+(-2\beta _{1}+2\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
152.3.u.b	$152$	$3$	152.u	152.u	$18$	$216$	$36$	$4.142$		$_{}$	None	None		$4$	$0$	\(-6\)	\(-18\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{18}]$
152.4.a.a	$152$	$4$	152.a	1.a	$1$	$2$	$2$	$8.968$	\(\Q(\sqrt{57}) \)	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-6\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-3+\beta )q^{5}+(-5+4\beta )q^{7}+\cdots\)
152.4.a.b	$152$	$4$	152.a	1.a	$1$	$3$	$3$	$8.968$	3.3.3221.1	$_{}$	None	None	✓	$1$	$1$	\(0\)	\(-5\)	\(2\)	\(-35\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
152.4.a.c	$152$	$4$	152.a	1.a	$1$	$3$	$3$	$8.968$	3.3.7057.1	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(4\)	\(7\)	\(7\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(2+2\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
152.4.a.d	$152$	$4$	152.a	1.a	$1$	$5$	$5$	$8.968$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(22\)	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
152.4.b.a	$152$	$4$	152.b	152.b	$2$	$2$	$2$	$8.968$	\(\Q(\sqrt{-2}) \)	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta q^{2}-2\beta q^{3}-8q^{4}+8q^{6}-2^{4}\beta q^{8}+\cdots\)
152.4.b.b	$152$	$4$	152.b	152.b	$2$	$56$	$56$	$8.968$		$_{}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
152.4.c.a	$152$	$4$	152.c	8.b	$2$	$54$	$54$	$8.968$		$_{}$	None	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(28\)			$\mathrm{SU}(2)[C_{2}]$
152.4.i.a	$152$	$4$	152.i	19.c	$3$	$14$	$7$	$8.968$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(5\)	\(5\)	\(-28\)		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{7})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots\)
152.4.i.b	$152$	$4$	152.i	19.c	$3$	$16$	$8$	$8.968$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-5\)	\(-8\)		$2^{12}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.4.o.a	$152$	$4$	152.o	152.o	$6$	$4$	$2$	$8.968$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$_{}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-30\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{6}]$	\(q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
152.4.o.b	$152$	$4$	152.o	152.o	$6$	$112$	$56$	$8.968$		$_{}$	None	None		$4$	$0$	\(-3\)	\(24\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$